Basis and Cost of Carry
Foreign exchange futures may have either a positive or negative cost of carry. Suppose, for example, that you are a U.S. importer needing to buy euros. You borrow dollars, your local currency, at the prevailing interest rate to buy euros, which you hold in an interest-bearing account until the date of the purchase. If you earn less interest on the euros than you pay in interest on the borrowed dollars, you have a negative carry. That is, it costs you to carry the euros. If your interest income is greater than your interest expense, then you have a positive carry.
The futures price that would accurately reflect the cost of carry is called its fair value and is calculated by the following formula:
The cost of carry is the cash price less the fair value of the futures contract.
|
Negative Carry |
Positive Carry |
|
terms rate > base rate |
terms rate < base rate |
|
borrowing cost > interest earned |
interest earned > borrowing cost |
|
basis is negative |
basis is positive |
|
futures trades at premium |
futures trades at discount |
|
fair value = spot price – (interest earned – borrowing cost) |
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Example: Assume that the cash price per euro in the foreign exchange (forex) market is $1.13, and the September futures price 90 days out is $1.14. The annual short-term interest rate in Germany is 2% and 3% in the U.S. The fair value of dollars is $1.1328. This is what the cash price should be in 90 days if the futures price accurately reflects the cost of carry:
The true cost of carry is the fair value of euro futures